JEE PYQ: Properties Of Triangle Question 1
Question 1 - 2021 (16 Mar Shift 2)
In $\triangle ABC$, the lengths of sides $AC$ and $AB$ are $12$ cm and $5$ cm, respectively. If the area of $\triangle ABC$ is $30$ cm$^2$ and $R$ and $r$ are respectively the radii of circumcircle and incircle of $\triangle ABC$, then the value of $2R + r$ (in cm) is equal to ______
Type: Numerical
Show Answer
Answer: 15
Solution
$\Delta = \frac{1}{2} \cdot 5 \cdot 12 \cdot \sin A = 30$
$\sin A = 1$, $A = 90^\circ \Rightarrow BC = 13$
$BC = 2R = 13$, $r = \frac{\Delta}{s} = \frac{30}{15} = 2$
$2R + r = 15$
BETA
